SOLUTION: Set up a system of linear equations and solve for the indicated quantities. Three times the smaller of two numbers plus 2 times the larger number is 27. Four times the smaller numb

Algebra.Com
Question 1124231: Set up a system of linear equations and solve for the indicated quantities. Three times the smaller of two numbers plus 2 times the larger number is 27. Four times the smaller number minus 2 times the larger number is -6. Find the numbers
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Follow the description exactly. You can decide how to assign variable or variables to what.

x, smaller number
y, larger number


You can solve that system.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Let x be the smaller and y be the greater number.


Then your system is


3x + 2y = 27,    (1)
4x - 2y = -6.    (2)


To solve it, add the equations (both sides).  You will get

3x + 4x = 27 - 6,    or

7x = 21  ====>    x = 21/7 = 3.


Then from eq(1),  2y = 27 - 3x = 27 - 3*3 = 18  and  y = 18/2 = 9.


Answer.  The smaller number is 3.  The greater number is 9.


RELATED QUESTIONS

Set up a system of linear equations and solve for the indicated quantities The sum of... (answered by ikleyn)
Set up a system of linear equations and solve for the indicated quantities. Two... (answered by josgarithmetic)
Set up a system of linear equations and solve for the indicated quantities The number... (answered by stanbon)
Set up a system of linear equations and solve for the indicated quantities Jim goes to (answered by josmiceli)
Set up a system of linear equations and solve for the indicated quantities. Nathan... (answered by MathLover1,ikleyn)
the sum of two numbers is 47. Find the two numbers if one is two more than four times... (answered by rfer)
Set up a system of linear equations in two variables to solve for the unknown quantities. (answered by ichigo449)
Translate the problem situation to a system of equations. Do not solve. The difference... (answered by SwiftAlbatross)
The sum of two numbers is 175. The larger number is three more than three times the... (answered by jojo14344)